How to create neural network that predicates result of exam?
You can add as many layers (with any arbitrary number of nodes) as you want.
Please note that as you add more learning parameters (layers and nodes), your model complexity increases. This means the model can potentially learn a more complex input-output relationship. However, it also increases the risk of overfitting. Overfitting generally happens when the model you build is more complex than the data you have. In such a scenario, the model memorizes the data instead of learning from it. In other words, it can produce a very good result for the same data as it was trained on but cannot generalize well. So, it performs poorly when the inputs are slightly different from what is used to be fed at the training stage.
In practice, you may try different architectures and parameter configurations, and measure the generalization capacity of the models (via cross-validation for example) to choose the best model. In English, a generalizable model is the one that performs (almost) equally good on both training/validation and testing sets.